A major snowstorm dumped more than a foot of snow in cities across the north-east US early Friday morning, causing thousands of flight cancellations, school closures and paralysing road travel.

New England was hardest hit, with Boston seeing 14 inches of snow while Boxford, 25 miles north, had received more than two feet by sunrise.

As the storm headed out over the Atlantic ocean, the National Weather Service warned that freezing temperatures would remain into the weekend. The wind chill could approach -50F (-45.6C) in parts of the mid-west over the weekend, the NWS said, while parts of New England could expect -20F (-28.9C).

Hundreds of schools were shut in Boston and New York City, while non-emergency Massachusetts state workers were told to stay at home.

The highest snow totals overnight came in Essex County, Massachusetts, where Boxford saw 24.3 inches of snow and Topsfield 23.5 inches, Boston.com reported. East Massachusetts had been expected to see increased snowfall due to an "ocean effect" of freezing northeasterly winds meeting the warmer Atlantic ocean.

There had been more than 1,725 flight cancellations and more than 900 delays by 9am, according to the Flight Aware monitoring website. The bulk of the cancellations were in Chicago, New York and Washington DC.

More than a foot of snow fell in parts of the mid-west before the storm sprawled across the north-east. The system brought freezing temperatures 20 to 30 degrees below the average for early January across the region. The NWS warned on Friday that "some of the coldest air of the year" would arrive in the northern tier of the US by Saturday.

"Forecast offices over [the upper mid-west] suggest lows into the -20s across North Dakota/Minnesota with breezy conditions lowering wind chills to dangerously low levels. Current guidance indicates wind chill temperatures may approach -50F on Saturday night," the NWS said in an alert.

In the north-east clean up efforts were expected to be hindered by freezing temperatures which could drop to a wind chill of -10F to -20F, the NWS said.

Public schools were closed in New York City, Boston and much of New England. New York and New Jersey declared state of emergencies as the storm approached, and New Jersey Governor Chris Christie ordered non-essential state workers to stay at home.

Amtrak planned to run trains on all of its north-east lines on Friday but operate on a modified schedule, spokeswoman Christina Leeds told the Associated Press.

The storm provided a first test of Bill De Blasio, New York City’s new mayor. His predecessor Michael Bloomberg had been criticised for his handling of a 2010 snow storm, when streets remained inaccessible for days in some parts of the city.

De Blasio had said his team was “focused like a laser” on protecting the city and initial reports on social media and local news appeared positive. There were 1,700 snow plows and 450 salt spreaders working the streets in New York City, De Blasio said.

In a press conference on Friday morning at a sanitation department depot in Queens, the mayor thanked John Doherty, the sanitation commissioner, and acknowledged the early test the storm had provided to his leadership.

"It would have been nice to have talked about how to handle a snowstorm in an abstract exercise, but we didn't get to do that, we got the real thing."

Sanitation workers were working 12-hour shifts to clear the roads, De Blasio said. As of 4am there were nearly 2,500 plows on the streets.

De Blasio said 100% of primary roads had been ploughed and 92% of secondary roads and 93% of tertiary roads. The mayor praised "an extraordinary level of performance" by the sanitation department in clearing streets but urged people to stay off the roads.

"If you do not need to travel today please stay home. If you do have to travel take mass transit. Yes there will be some delays but it will be safe."

Temperatures remain "deceptively cold", De Blasio said as he urged New Yorkers not to underestimate the freezing conditions. "It's as cold as it's been all year. If you stay out there too long it will be bad and it will be dangerous."

The mayor said he had shovelled snow himself this morning before his son, Dante, took over.

He also denied that the city had concentrated its snow-clearing efforts on the outer boroughs at the expense of Manhattan. "You have a rich imagination," he told the reporter who asked the question.

After the 2010 blizzard, Bloomberg was heavily criticised for clearing Manhattan streets first.